Information about Surface Gravity
The surface gravity, g, of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in order not to disturb the system, has negligible mass.
The dimensional units of gravitational acceleration are meters per square second. However as noted in the formula below, the conventional number used to describe the surface gravity of an object is expressed as a ratio of its mass and mean radius to that of the Earth. Thus while the mean force of gravity on the surface of the earth is somewhat less than 10 meters per square second, using the relative measure it is (a dimensionless) 1 g.
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A large object, such as a planet or star, will usually be approximately round, because large mountains will be squashed down, and large valleys filled in, by the object's own gravity. This hydrostatic equilibrium condition usually also applies to changes of density inside the object, so that the density at a place inside the object will depend only on how far it is from the object's center. If this is so, the object is called spherically symmetric.[1] The gravitational force outside a spherically symmetric body is the same as if its entire mass were concentrated in the center, as was established by Sir Isaac Newton.[2] Therefore, the surface gravity of a planet or star will be approximately inversely proportional to the square of its radius. For example, the recently-discovered planet, Gliese 581 c, has at least 5 times the mass of Earth, but is unlikely to have 5 times its surface gravity. If its mass is no more than 5 times that of the Earth, as is expected[3], and if it is a rocky planet with a large iron core, it should have a radius approximately 50% larger than that of Earth.[4][5] Gravity on such a planet's surface would be approximately 2.2 times as strong as on Earth. If it is an icy or watery planet, its radius might be as large as twice the Earth's, in which case its surface gravity might be no more than 1.25 times as strong as the Earth's.<ref name="model" />
These proportionalities may be expressed by the formula g = m/r2, where g is the surface gravity of an object, expressed as a multiple of the Earth's, m is its mass, expressed as a multiple of the Earth's mass (5.976·1024 kg) and r its radius, expressed as a multiple of the Earth's (mean) radius (6371 km).[6] For instance, Mars has a mass of 6.4185·1023 kg = 0.107 Earth masses and a mean radius of 3390 km = 0.532 Earth radii.[7] The surface gravity of Mars is therefore approximately
Since gravity is inversely proportional to the square of the distance, a space station 100 miles above the Earth feels almost the same gravitational force as we do on the Earth's surface. The reason a space station does not plummet to the ground is not that it is not subject to gravity, but that it is in a free-fall orbit. This would not be true of a space elevator—a concept you can find explained in the SF novel The Fountains of Paradise, written by Sir Arthur C. Clarke, who has a good understanding of the physics and engineering involved.
To the extent that an object's internal distribution of mass differs from a symmetric model, we may use the measured surface gravity to deduce things about the object's internal structure. This fact has been put to practical use since 1915–1916, when Roland Eötvös's torsion balance was used to prospect for oil near the city of Egbell (now Gbely, Slovakia.)[8], p. 1663;[9], p. 223. In 1924, the torsion balance was used to locate the Nash Dome oil fields in Texas.<ref name="hung" />, p. 223.
It is sometimes useful to calculate the surface gravity of simple hypothetical objects which are not found in nature. The surface gravity of infinite planes, tubes, lines, hollow shells, cones, and even more unrealistic structures may be used to provide insights into the behavior of real structures.
The surface gravity
of a Killing horizon is the acceleration, as exerted at infinity, needed to keep an object at the horizon. Mathematically, if 
is a suitably normalized Killing vector, then the surface gravity is defined by
where the equation is evaluated at the horizon. For a static and asymptotically flat spacetime, the normalization should be chosen so that
as 
, and so that 
. For the Schwarzschild solution, we take to be the time translation Killing vector 
, and more generally for the Kerr-Newman solution we take 
, the linear combination of the time translation and axisymmetry Killing vectors which is null at the horizon, where 
is the angular velocity.
is a Killing vector 
implies 
. In 
coordinates 
. Performing a coordinate change to the advanced Eddington-Finklestein coordinates 
causes the metric to take the form 
.
Under a general change of coordinates the Killing vector transforms as
giving the vectors 
and 
Considering the b=r entry for
gives the differential equation 
Therefore the surface gravity for the Schwarzschild solution with mass
is 
.
where
is the electric charge, 
is the angular velocity, we define 
to be the locations of the two horizons and 
.
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The dimensional units of gravitational acceleration are meters per square second. However as noted in the formula below, the conventional number used to describe the surface gravity of an object is expressed as a ratio of its mass and mean radius to that of the Earth. Thus while the mean force of gravity on the surface of the earth is somewhat less than 10 meters per square second, using the relative measure it is (a dimensionless) 1 g.
Mass, radius and surface gravity
In the Newtonian theory of gravity, the gravitational force exerted by an object is proportional to its mass: an object with twice the mass produces twice as much force. Newtonian gravity also follows an inverse square law, so that moving an object twice as far away divides its gravitational force by four, and moving it ten times as far away divides it by 100. This is similar to the intensity of light, which also follows an inverse square law: lights far away give the observer less light.A large object, such as a planet or star, will usually be approximately round, because large mountains will be squashed down, and large valleys filled in, by the object's own gravity. This hydrostatic equilibrium condition usually also applies to changes of density inside the object, so that the density at a place inside the object will depend only on how far it is from the object's center. If this is so, the object is called spherically symmetric.[1] The gravitational force outside a spherically symmetric body is the same as if its entire mass were concentrated in the center, as was established by Sir Isaac Newton.[2] Therefore, the surface gravity of a planet or star will be approximately inversely proportional to the square of its radius. For example, the recently-discovered planet, Gliese 581 c, has at least 5 times the mass of Earth, but is unlikely to have 5 times its surface gravity. If its mass is no more than 5 times that of the Earth, as is expected[3], and if it is a rocky planet with a large iron core, it should have a radius approximately 50% larger than that of Earth.[4][5] Gravity on such a planet's surface would be approximately 2.2 times as strong as on Earth. If it is an icy or watery planet, its radius might be as large as twice the Earth's, in which case its surface gravity might be no more than 1.25 times as strong as the Earth's.<ref name="model" />
These proportionalities may be expressed by the formula g = m/r2, where g is the surface gravity of an object, expressed as a multiple of the Earth's, m is its mass, expressed as a multiple of the Earth's mass (5.976·1024 kg) and r its radius, expressed as a multiple of the Earth's (mean) radius (6371 km).[6] For instance, Mars has a mass of 6.4185·1023 kg = 0.107 Earth masses and a mean radius of 3390 km = 0.532 Earth radii.[7] The surface gravity of Mars is therefore approximately
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Since gravity is inversely proportional to the square of the distance, a space station 100 miles above the Earth feels almost the same gravitational force as we do on the Earth's surface. The reason a space station does not plummet to the ground is not that it is not subject to gravity, but that it is in a free-fall orbit. This would not be true of a space elevator—a concept you can find explained in the SF novel The Fountains of Paradise, written by Sir Arthur C. Clarke, who has a good understanding of the physics and engineering involved.
Non-spherically symmetric objects
Most real astronomical objects are not absolutely spherically symmetric. One reason for this is that they are often rotating, which means that they are affected by the combined effects of gravitational force and centrifugal force. This causes stars and planets to be oblate, which means that their surface gravity is smaller at the equator than at the poles. This effect was exploited by Hal Clement in his SF novel Mission of Gravity, dealing with a massive, fast-spinning planet where gravity was much higher at the poles than at the equator.To the extent that an object's internal distribution of mass differs from a symmetric model, we may use the measured surface gravity to deduce things about the object's internal structure. This fact has been put to practical use since 1915–1916, when Roland Eötvös's torsion balance was used to prospect for oil near the city of Egbell (now Gbely, Slovakia.)[8], p. 1663;[9], p. 223. In 1924, the torsion balance was used to locate the Nash Dome oil fields in Texas.<ref name="hung" />, p. 223.
It is sometimes useful to calculate the surface gravity of simple hypothetical objects which are not found in nature. The surface gravity of infinite planes, tubes, lines, hollow shells, cones, and even more unrealistic structures may be used to provide insights into the behavior of real structures.
Units
Gravity is measured in units of acceleration, which, in the SI system, are meters per second squared. It may also be expressed as a multiple of the Earth's standard surface gravity (which, confusingly, is also often called g), or, in astrophysics, as log g, obtained by first expressing the gravity in cgs units, where the unit of acceleration is centimeters per second squared, and then taking the base 10 logarithm.[10]Surface gravity of a black hole
The surface gravity
of a Killing horizon is the acceleration, as exerted at infinity, needed to keep an object at the horizon. Mathematically, if is a suitably normalized Killing vector, then the surface gravity is defined by
,
where the equation is evaluated at the horizon. For a static and asymptotically flat spacetime, the normalization should be chosen so that
as , and so that . For the Schwarzschild solution, we take to be the time translation Killing vector , and more generally for the Kerr-Newman solution we take , the linear combination of the time translation and axisymmetry Killing vectors which is null at the horizon, where is the angular velocity.
The Schwarzschild solution
Since is a Killing vector implies . In coordinates . Performing a coordinate change to the advanced Eddington-Finklestein coordinates causes the metric to take the form .
Under a general change of coordinates the Killing vector transforms as
giving the vectors and
Considering the b=r entry for
gives the differential equation
Therefore the surface gravity for the Schwarzschild solution with mass
is .
The Kerr-Newman solution
The surface gravity for the Kerr-Newman solution is
,
where
is the electric charge, is the angular velocity, we define to be the locations of the two horizons and .
References
1. ^ Why is the Earth round?, at Ask A Scientist, accessed online May 27, 2007.
2. ^ Book I, §XII, pp. 218–226, Newton's Principia: The Mathematical Principles of Natural Philosophy, Sir Isaac Newton, tr. Andrew Motte, ed. N. W. Chittenden. New York: Daniel Adee, 1848. First American edition.
3. ^ Astronomers Find First Earth-like Planet in Habitable Zone, ESO 22/07, press release from the European Southern Observatory, April 25, 2007
4. ^ The HARPS search for southern extra-solar planets XI. Super-Earths (5 & 8 M_Earth) in a 3-planet system, S. Udry, X. Bonfils), X. Delfosse, T. Forveille, M. Mayor, C. Perrier, F. Bouchy, C. Lovis, F. Pepe, D. Queloz, and J.-L. Bertaux. arXiv:astro-ph/0704.3841.
5. ^ Detailed Models of super-Earths: How well can we infer bulk properties?, Diana Valencia, Dimitar D. Sasselov, and Richard J. O'Connell, arXiv:astro-ph/0704.3454.
6. ^ 2.7.4 Physical properties of the Earth, web page, accessed on line May 27, 2007.
7. ^ Mars Fact Sheet, web page at NASA NSSDC, accessed May 27, 2007.
8. ^ Ellipsoid, geoid, gravity, geodesy, and geophysics, Xiong Li and Hans-Jürgen Götze, Geophysics, 66, #6 (November–December 2001), pp. 1660–1668. DOI 10.1190/1.1487109.
9. ^ Prediction by Eötvös' torsion balance data in Hungary, Gyula Tóth, Periodica Polytechnica Ser. Civ. Eng. 46, #2 (2002), pp. 221–229.
10. ^ Smalley, B. (2006-07-13). The Determination of Teff and log g for B to G stars. Keele University. Retrieved on 2007-05-31.
2. ^ Book I, §XII, pp. 218–226, Newton's Principia: The Mathematical Principles of Natural Philosophy, Sir Isaac Newton, tr. Andrew Motte, ed. N. W. Chittenden. New York: Daniel Adee, 1848. First American edition.
3. ^ Astronomers Find First Earth-like Planet in Habitable Zone, ESO 22/07, press release from the European Southern Observatory, April 25, 2007
4. ^ The HARPS search for southern extra-solar planets XI. Super-Earths (5 & 8 M_Earth) in a 3-planet system, S. Udry, X. Bonfils), X. Delfosse, T. Forveille, M. Mayor, C. Perrier, F. Bouchy, C. Lovis, F. Pepe, D. Queloz, and J.-L. Bertaux. arXiv:astro-ph/0704.3841.
5. ^ Detailed Models of super-Earths: How well can we infer bulk properties?, Diana Valencia, Dimitar D. Sasselov, and Richard J. O'Connell, arXiv:astro-ph/0704.3454.
6. ^ 2.7.4 Physical properties of the Earth, web page, accessed on line May 27, 2007.
7. ^ Mars Fact Sheet, web page at NASA NSSDC, accessed May 27, 2007.
8. ^ Ellipsoid, geoid, gravity, geodesy, and geophysics, Xiong Li and Hans-Jürgen Götze, Geophysics, 66, #6 (November–December 2001), pp. 1660–1668. DOI 10.1190/1.1487109.
9. ^ Prediction by Eötvös' torsion balance data in Hungary, Gyula Tóth, Periodica Polytechnica Ser. Civ. Eng. 46, #2 (2002), pp. 221–229.
10. ^ Smalley, B. (2006-07-13). The Determination of Teff and log g for B to G stars. Keele University. Retrieved on 2007-05-31.
External links
Astronomical objects are significant physical entities, associations or structures which current science has confirmed to exist in space. This does not necessarily mean that more current science will not disprove their existence.
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In physics, gravitational acceleration is the acceleration of an object caused by the force of gravity from another object. An interesting fact is that any object will accelerate towards a large object at the same rate, regardless of the mass of the object.
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Isaac Newton's theory of universal gravitation is a physical law describing the gravitational attraction between massive bodies. It is a part of classical mechanics and was first formulated in Newton's work Philosophiae Naturalis Principia Mathematica, published in 1687.
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Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight.
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Isaac Newton's theory of universal gravitation is a physical law describing the gravitational attraction between massive bodies. It is a part of classical mechanics and was first formulated in Newton's work Philosophiae Naturalis Principia Mathematica, published in 1687.
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Light is electromagnetic radiation of a wavelength that is visible to the eye (visible light). In a scientific context, the word "light" is sometimes used to refer to the entire electromagnetic spectrum.
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planet, as defined by the International Astronomical Union (IAU), is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, not massive enough to cause thermonuclear fusion in its core, and has cleared its neighbouring region of
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STAR is an acronym for:
Organizations:
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Organizations:
- Society for Telescopy, Astronomy, and Radio, a non-profit astronomy club in New Jersey
- Special Tasks and Rescue or Special Tactics and Response, synonyms for SWAT
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Hydrostatic equilibrium occurs when compression due to gravity is balanced by a pressure gradient which creates a pressure gradient force in the opposite direction. The balance of these two forces is known as the hydrostatic balance.
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In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of
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In mechanics and geometry, the rotation group is the group of all rotations about the origin of 3-dimensional Euclidean space R3 under the operation of composition.
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Sir Isaac Newton
Isaac Newton at 46 in
Godfrey Kneller's 1689 portrait
Born 4 January 1643 [OS: 25 December 1642]
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Isaac Newton at 46 in
Godfrey Kneller's 1689 portrait
Born 4 January 1643 [OS: 25 December 1642]
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planet, as defined by the International Astronomical Union (IAU), is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, not massive enough to cause thermonuclear fusion in its core, and has cleared its neighbouring region of
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STAR is an acronym for:
Organizations:
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Organizations:
- Society for Telescopy, Astronomy, and Radio, a non-profit astronomy club in New Jersey
- Special Tasks and Rescue or Special Tactics and Response, synonyms for SWAT
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In classical geometry, a radius (plural: radii) of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment. The radius is half the diameter.
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planet, as defined by the International Astronomical Union (IAU), is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, not massive enough to cause thermonuclear fusion in its core, and has cleared its neighbouring region of
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Gliese 581 c (IPA: /ˈgliːzə/), also unofficially known as Ymir[3], is a "super-earth" extrasolar planet orbiting the red dwarf star Gliese 581.
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EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001. Their greatest hit, their debut single "time after time", peaked at #13 in the Oricon singles chart.
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EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001. Their greatest hit, their debut single "time after time", peaked at #13 in the Oricon singles chart.
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kilogram or kilogramme (symbol: kg) is the SI base unit of mass. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water.
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1 kilometre =
SI units
0 m 0106 mm
US customary / Imperial units
0 ft 0 mi
A kilometre (American spelling: kilometer, symbol kmSI units
0 m 0106 mm
US customary / Imperial units
0 ft 0 mi
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Mars
Mars as seen by the Hubble Space Telescope
Orbital characteristics
Epoch J2000<ref name="nssdc" />
Aphelion distance: 249,228,730 km
1.66599116 AU
Perihelion distance: 206,644,545 km
1.
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Mars as seen by the Hubble Space Telescope
Orbital characteristics
Epoch J2000<ref name="nssdc" />
Aphelion distance: 249,228,730 km
1.66599116 AU
Perihelion distance: 206,644,545 km
1.
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kilogram or kilogramme (symbol: kg) is the SI base unit of mass. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water.
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Isaac Newton's theory of universal gravitation is a physical law describing the gravitational attraction between massive bodies. It is a part of classical mechanics and was first formulated in Newton's work Philosophiae Naturalis Principia Mathematica, published in 1687.
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gravitational constant, the universal gravitational constant, Newton's constant, and colloquially Big G. The gravitational constant is a physical constant which appears in Newton's law of universal gravitation and in Einstein's theory of general
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Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight.
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Free fall is motion with no acceleration other than that provided by gravity. This also applies to objects in orbit, even though these objects are not "falling" in the usual sense of the word.
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ORBit is a CORBA compliant Object Request Broker (ORB). The current version is called ORBit2 and is compliant with CORBA version 2.4. It is developed under the GPL license and is used as middleware for the GNOME project.
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space elevator is a proposed megastructure designed to transport material from a celestial body's surface into space, first conceived by Konstantin Tsiolkovsky.[1] Many different types of space elevators have been suggested.
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The Fountains of Paradise
Cover of first UK edition (hardcover)
Author Arthur C. Clarke
Country United Kingdom
Language English
Genre(s) Science fiction novel
Publisher Victor Gollancz (UK) &
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Cover of first UK edition (hardcover)
Author Arthur C. Clarke
Country United Kingdom
Language English
Genre(s) Science fiction novel
Publisher Victor Gollancz (UK) &
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Herod_Archelaus
